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In high-current induction accelerators being considered for heavy ion inertial fusion and other applications, the resistive-wall instability in the long-wavelength range, may cause unacceptable beam energy spread. We have designed a small-scale low-cost electron beam experiment to investigate this instability in 1 m, 5 10 kV resistive-wall structures. In this Letter, we present the first experimental results on the interaction between a resistive wall and localized single space-charge waves in the longwavelength range. The experiments have clearly demonstrated the growth of single slow waves due to the resistive-wall instability and the decay of single fast waves. The spatial growth/decay rates are measured and compared with theoretical analysis. [S0031-9007(97)03756-3]